Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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A NEW QUARTERNIONIC DIRAC OPERATOR ON SYMPLECTIC SUBMANIFOLD OF A PRODUCT SYMPLECTIC MANIFOLD

  • Received : 2023.10.18
  • Accepted : 2024.02.16
  • Published : 2024.03.30
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Abstract

The Quaternionic Dirac operator proves instrumental in tackling various challenges within spectral geometry processing and shape analysis. This work involves the introduction of the quaternionic Dirac operator on a symplectic submanifold of an exact symplectic product manifold. The self adjointness of the symplectic quaternionic Dirac operator is observed. This operator is verified for spin ${\frac{1}{2}}$ particles. It factorizes the Hodge Laplace operator on the symplectic submanifold of an exact symplectic product manifold. For achieving this a new complex structure and an almost quaternionic structure are formulated on this exact symplectic product manifold.

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References

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